Squared Earth Mover's Distance-based Loss for Training Deep Neural Networks

TL;DR

This paper introduces a squared Earth Mover's Distance loss for training deep neural networks that accounts for inter-class relationships, improving performance especially on datasets with ordered classes, and includes a method to learn this relationship automatically.

Contribution

It proposes a novel squared EMD loss for deep learning that incorporates class relationships and a method to learn the ground distance matrix during training.

Findings

Achieves state-of-the-art results on datasets with inter-class relationships.

Automatically learning the class dissimilarity matrix yields comparable performance.

Maintains high performance even without strong inter-class relationships.

Abstract

In the context of single-label classification, despite the huge success of deep learning, the commonly used cross-entropy loss function ignores the intricate inter-class relationships that often exist in real-life tasks such as age classification. In this work, we propose to leverage these relationships between classes by training deep nets with the exact squared Earth Mover's Distance (also known as Wasserstein distance) for single-label classification. The squared EMD loss uses the predicted probabilities of all classes and penalizes the miss-predictions according to a ground distance matrix that quantifies the dissimilarities between classes. We demonstrate that on datasets with strong inter-class relationships such as an ordering between classes, our exact squared EMD losses yield new state-of-the-art results. Furthermore, we propose a method to automatically learn this matrix using the CNN's own features during training. We show that our method can learn a ground distance matrix efficiently with no inter-class relationship priors and yield the same performance gain. Finally, we show that our method can be generalized to applications that lack strong inter-class relationships and still maintain state-of-the-art performance. Therefore, with limited computational overhead, one can always deploy the proposed loss function on any dataset over the conventional cross-entropy.